Height and Distance Calculator

Solve trigonometry problems involving height and distance. Calculate angle of elevation, depression, height of objects, distances between objects, and solve real-world applications.

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Angle of Elevation Calculator

Calculate angle of elevation when observer looks upward at an object. Height and distance inputs required.

Angle of Depression Calculator

Calculate angle of depression when observer looks downward from an elevated position.

Height of Object Calculator

Calculate height of objects like buildings, trees, or poles using trigonometry methods.

Distance Between Objects

Calculate distance between two objects using angles of elevation/depression from observation points.

Trigonometric Ratios

Calculate sin, cos, tan, cosec, sec, cot for any angle. Useful for height and distance problems.

Real-World Applications

Solve practical height and distance problems from real-world scenarios.

Height and Distance Formulas Reference

Essential trigonometric formulas for solving height and distance problems.

Basic Formulas

Height from Angle & Distance
h = d × tan(θ)
θ = angle of elevation, d = distance
Distance from Height & Angle
d = h ÷ tan(θ)
or d = h × cot(θ)
Angle from Height & Distance
θ = tan⁻¹(h ÷ d)
Inverse tangent function

Two Angles Method

Height using Two Angles
h = d × [tan(θ₁) × tan(θ₂)] ÷ [tan(θ₂) - tan(θ₁)]
When moving towards object
Distance between Points
d = h × [cot(θ₁) - cot(θ₂)]
For two observation points

Trigonometric Ratios

Right Triangle Ratios
sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent
Reciprocal Ratios
cosec(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)

Special Angles

Common Angle Values
sin(30°) = 1/2, cos(30°) = √3/2
sin(45°) = cos(45°) = 1/√2
sin(60°) = √3/2, cos(60°) = 1/2
tan(θ) = sin(θ)/cos(θ)